On Singular Yamabe Obstructions

Andreas Juhl; Bent Ørsted

doi:10.1007/s12220-022-00867-6

On Singular Yamabe Obstructions

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

We discuss the obstruction to the existence of a smooth solution of a singular version of the Yamabe problem for a hypersurface in a four-dimensional general background. This obstruction is a conformally invariant density. We derive various explicit formulas for the singular Yamabe obstruction directly from the original definition. We discuss in detail the relation to results in the literature.

Originalsprog	Engelsk
Artikelnummer	146
Tidsskrift	Journal of Geometric Analysis
Vol/bind	32
Nummer	5
ISSN	1050-6926
DOI	https://doi.org/10.1007/s12220-022-00867-6
Status	Udgivet - maj 2022

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10.1007/s12220-022-00867-6

https://arxiv.org/pdf/2103.01552.pdf

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abstract = "We discuss the obstruction to the existence of a smooth solution of a singular version of the Yamabe problem for a hypersurface in a four-dimensional general background. This obstruction is a conformally invariant density. We derive various explicit formulas for the singular Yamabe obstruction directly from the original definition. We discuss in detail the relation to results in the literature.",

keywords = "Conformal geometry, Hypersurface invariant, Poincar{\'e}–Einstein metric, Singular Yamabe problem, Willmore functional, Yamabe obstruction",

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AU - Ørsted, Bent

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KW - Conformal geometry

KW - Hypersurface invariant

KW - Poincaré–Einstein metric

KW - Singular Yamabe problem

KW - Willmore functional

KW - Yamabe obstruction

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On Singular Yamabe Obstructions

Abstract

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